Answer:
a. Kp=1.4
![P_{A}=0.2215 atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D0.2215%20atm)
![P_{B}=0.556 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D0.556%20atm)
b.Kp=2.0 * 10^-4
![P_{A}=0.495atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D0.495atm)
![P_{B}=0.00995 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D0.00995%20atm)
c.Kp=2.0 * 10^5
![P_{A}=5*10^{-6}atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D5%2A10%5E%7B-6%7Datm)
![P_{B}=0.9999 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D0.9999%20atm)
Explanation:
For the reaction
A(g)⇌2B(g)
Kp is defined as:
![Kp=\frac{(P_{B})^{2}}{P_{A}}](https://tex.z-dn.net/?f=Kp%3D%5Cfrac%7B%28P_%7BB%7D%29%5E%7B2%7D%7D%7BP_%7BA%7D%7D)
The conditions in the system are:
A B
initial 0 1 atm
equilibrium x 1atm-2x
At the beginning, we don’t have any A in the system, so B starts to react to produce A until the system reaches the equilibrium producing x amount of A. From the stoichiometric relationship in the reaction we get that to produce x amount of A we need to 2x amount of B so in the equilibrium we will have 1 atm – 2x of B, as it is showed in the table.
Replacing these values in the expression for Kp we get:
![Kp=\frac{(1-2x)^{2}}{x}](https://tex.z-dn.net/?f=Kp%3D%5Cfrac%7B%281-2x%29%5E%7B2%7D%7D%7Bx%7D)
Working with this equation:
![x*Kp=(1-2x)^{2} - -> x*Kp=4x^{2}-4x+1- - >4x^{2}-(4+Kp)*x+1=0](https://tex.z-dn.net/?f=x%2AKp%3D%281-2x%29%5E%7B2%7D%20-%20-%3E%20x%2AKp%3D4x%5E%7B2%7D-4x%2B1-%20-%20%3E4x%5E%7B2%7D-%284%2BKp%29%2Ax%2B1%3D0)
This last expression is quadratic expression with a=4, b=-(4+Kp) and c=1
The general expression to solve these kinds of equations is:
(equation 1)
We just take the positive values from the solution since negative partial pressures don´t make physical sense.
Kp = 1.4
![x_{1}=\frac{(1.4+4)+\sqrt{(-(1.4+4)^{2}-4*4*1)}}{2*4}=1.128](https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Cfrac%7B%281.4%2B4%29%2B%5Csqrt%7B%28-%281.4%2B4%29%5E%7B2%7D-4%2A4%2A1%29%7D%7D%7B2%2A4%7D%3D1.128)
![x_{1}=\frac{(1.4+4)-\sqrt{(-(1.4+4)^{2}-4*4*1)}}{2*4}=0.2215](https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Cfrac%7B%281.4%2B4%29-%5Csqrt%7B%28-%281.4%2B4%29%5E%7B2%7D-4%2A4%2A1%29%7D%7D%7B2%2A4%7D%3D0.2215)
With x1 we get a partial pressure of:
![P_{A}=1.128 atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D1.128%20atm)
![P_{B}=1-2*1.128 = -1.256 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D1-2%2A1.128%20%3D%20-1.256%20atm)
Since negative partial pressure don´t make physical sense x1 is not the solution for the system.
With x2 we get:
![P_{A}=0.2215 atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D0.2215%20atm)
![P_{B}=1-2*0.2215 = 0.556 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D1-2%2A0.2215%20%3D%200.556%20atm)
These partial pressures make sense so x2 is the solution for the equation.
We follow the same analysis for the other values of Kp.
Kp=2*10^-4
X1=0.505
X2=0.495
With x1
![P_{A}=0.505atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D0.505atm)
![P_{B}=1-2*0.505 = -0.01005 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D1-2%2A0.505%20%3D%20-0.01005%20atm)
Not sense.
With x2
![P_{A}=0.495atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D0.495atm)
![P_{B}=1-2*0.495 = 0.00995 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D1-2%2A0.495%20%3D%200.00995%20atm)
X2 is the solution for this equation.
Kp=2*10^5
X1=50001
![X2=5*10^{-6}](https://tex.z-dn.net/?f=X2%3D5%2A10%5E%7B-6%7D)
With x1
![P_{A}=50001atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D50001atm)
![P_{B}=1-2*50001=-100001atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D1-2%2A50001%3D-100001atm)
Not sense.
With x2
![P_{A}= 5*10^{-6}atm](https://tex.z-dn.net/?f=P_%7BA%7D%3D%205%2A10%5E%7B-6%7Datm)
![P_{B}=1-2*5*10^{-6}= 0.9999 atm](https://tex.z-dn.net/?f=P_%7BB%7D%3D1-2%2A5%2A10%5E%7B-6%7D%3D%200.9999%20atm)
X2 is the solution for this equation.
<h3>
Answer:</h3>
5.55 mol C₂H₅OH
<h3>
General Formulas and Concepts:</h3>
<u>Math</u>
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Chemistry</u>
<u>Atomic Structure</u>
- Reading a Periodic Tables
- Moles
<u>Stoichiometry</u>
- Using Dimensional Analysis
- Analyzing Reactions RxN
<h3>
Explanation:</h3>
<u>Step 1: Define</u>
[RxN - Balanced] C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
[Given] 500. g C₆H₁₂O₆ (Glucose)
[Solve] moles C₂H₅OH (Ethanol)
<u>Step 2: Identify Conversions</u>
[RxN] 1 mol C₆H₁₂O₆ → 2 mol C₂H₅OH
[PT] Molar mass of C - 12.01 g/mol
[PT] Molar Mass of H - 1.01 g/mol
[PT] Molar Mass of O - 16.00 g/mol
Molar Mass of C₆H₁₂O₆ - 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol
<u>Step 3: Stoichiometry</u>
- [DA] Set up conversion:
![\displaystyle 500 \ g \ C_6H_{12}O_6(\frac{1 \ mol \ C_6H_{12}O_6}{180.18 \ g \ C_6H_{12}O_6})(\frac{2 \ mol \ C_2H_5OH}{1 \ mol \ C_6H_{12}O_6})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20500%20%5C%20g%20%5C%20C_6H_%7B12%7DO_6%28%5Cfrac%7B1%20%5C%20mol%20%5C%20C_6H_%7B12%7DO_6%7D%7B180.18%20%5C%20g%20%5C%20C_6H_%7B12%7DO_6%7D%29%28%5Cfrac%7B2%20%5C%20mol%20%5C%20C_2H_5OH%7D%7B1%20%5C%20mol%20%5C%20C_6H_%7B12%7DO_6%7D%29)
- [DA} Multiply/Divide [Cancel out units]:
![\displaystyle 5.55001 \ mol \ C_2H_5OH](https://tex.z-dn.net/?f=%5Cdisplaystyle%205.55001%20%5C%20mol%20%5C%20C_2H_5OH)
<u>Step 4: Check</u>
<em>Follow sig fig rules and round. We are given 3 sig figs.</em>
5.55001 mol C₂H₅OH ≈ 5.55 mol C₂H₅OH
Answer:
The answer to your question is: SiCl₄
Explanation:
Data
amount of Si 1.71 g
amount of Cl 8.63 g
MW Si = 28 g
MW Cl = 35.5
Process (rule of three)
For Si For Cl
28 g of Si ------------------ 1 mol 35.5 g of Cl --------------- 1 mol
1.71g of Si --------------- x 8.63 g of Cl -------------- x
x = 1.71 x 1 / 28 = 0.06 mol x = 8.63 x 1 / 35.5 = 0.24 mol
Now, divide both results by the lowest of them.
Si = 0.06 mol / 0.06 = 1 molecule of Si Cl = 0.24 / 0.06 = 4 molecules of Cl
Finally
Si₁ Cl₄ or SiCl₄